3. Laurie uses yellow and white tiles to create a pattern.
a) Make a table of values to show the number of yellow tiles in relation to the figure number.
b) Describe the relationship between the number of yellow tiles and the figure number.
c) Develop an expression and an equation to model the number of yellow tiles. Explain what each part of the equation represents.
d) How many yellow tiles are in Figure 24?
e) Which figure number has 176 yellow tiles? Verify your answer.
f) Is it possible to have a figure with 54 yellow tiles? Show how you know.

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

(a) The value of the z-score for the 6.4 fluid ounce orange is -1.64

(b) The value of the z-score for the 3.11 fluid ounce orange is -4.63

From the question, we have the following parameters that can be used in our computation:

Mean = 8.2

Standard deviation = 1.1

The values of the z-scores is calculated as

z = (z - Mean)/Standard deviation

So, we have

z = (z - 8.2)/1.1

When the score is 6.4, we have

z = (6.4 - 8.2)/1.1

Evaluate

z = -1.64

Recall that

z = (z - Mean)/Standard deviation

So when the score is 3.11, we have

z = (3.11 - 8.2)/1.1

Evaluate the expression

z = -4.63

Hence, the values of the z-scores are -1.64 and -4.63

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The midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.

Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:

D = (B + C) / 2

E = (A + C) / 2

F = (A + B) / 2

To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:

1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)

Expanding the equation further:

1/3(a + b + c) = 1/3(3F - 2D - E + b + c)

= (F - (2/3)D - (1/3)E) + (1/3)(b + c)

Therefore, the point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

Substituting the midpoints:

P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)

= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)

= (b + c - B - C) / 2 + (1/3)(b + c)

Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

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Answer:

-3.5 and -0.5 would be the answers

The statements that would support her request include:

A well-known marker brand's manufacturer intends to introduce a new shade. It mailed surveys to 5,000 of its customers asking them which general color family they preferred in order to decide which color to add.

The percentage difference is not statistically significant enough to support the majority claim. The survey did not include families of every color, which might have led to nonresponse bias.

It's possible that the mail-in survey had an undercoverage bias. Also, the results were not random because only current clients were polled.

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Answer: the other guy is correct except for the "since only existing customers...".

Step-by-step explanation:

Just took the test, the others he mentioned were right

Y-intercept = -4

Slope = 2/3

Answer:

y-intercept = -4; slope = 2/3

Step-by-step explanation:

The graph crosses the y-axis at -4, so the y-intercept is -4.

Now we use the y-intercept and the x-intercept to find the slope.

Start at the y-intercept which is point (0, -4). Go up 4 units until you reach the x-axis. Going vertically up is a positive rise of 4 units. Now go right until you reach the x-intercept which is point (6, 0). Going 6 units to the right is a positive run of 6 units.

slope = rise/run

slope = 4/6 = 2/3

Answer: y-intercept = -4; slope = 2/3

The volume generated by rotating the given region \(R_{3}\) about OC is \(\frac{4}{g} \pi\)

Because the given region (\(R_{3}\)) has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.

solution

We first find the value of x and y

\(y=2(x)^{\frac{1}{4} }\)

\(x=(\frac{y}{2} )^{4}\)

\(y=2x\)

\(x=\frac{y}{2}\)

\(\int\limits^a_b {\pi } \, (R_{o^{2} } - R_{i^{2} } ) dy\)

\(R_{o} = x = \frac{y}{2}\)

\(R_{i} = x= (\frac{y}{2}) ^{4}\)

\(a=0, b=2\)

\(v= \int\limits^2_o {\pi } \, [(\frac{y}{2})^{2} - ((\frac{y}{2}) ^{4} )^{2} ) dy\)

\(v= \pi \int\limits^2_o= [\frac{y^{2} }{4} - \frac{y^{8} }{2^{8} }} ] dy\)

\(v= \pi [\int\limits^2_o {\frac{y^{2} }{4} } \, dy - \int\limits^2_o {\frac{y}{2^{8} } ^{8} } \, dy ]\)

\(v=\pi [\frac{1}{4} \frac{y^{3} }{3} \int\limits^2_0 - \frac{1}{2^{8} } \frac{y^{g} }{g} \int\limits^2_o\\v= \pi [\frac{1}{12} (2^{3} -0)-\frac{1}{2^{8}*9 } (2^{g} -0)]\\v= \pi [\frac{2}{3} -\frac{2}{g} ]\\v= \frac{4}{g} \pi\)

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A sequence of transformations that maps △ABC to △A′B′C′ is a rotation of 90° counterclockwise about the origin followed by a translation 2 units right.

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation

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A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.

The sequence of vertices ABC(DEF in this question) is clockwise, as is the sequence of A'B'C'(D'E'F in this question). Thus, an even number of reflections is involved, if any reflections are involved. The offered choices do not include suitable reflections.

The orientation of AB(DE) is toward the right. The orientation of A'B'(D'E') is up, so there must be a rotation of 90° CCW. Rotation of 90° CCW about the origin will leave the figure in a position that is 2 units left of where it is shown. The rotation must be followed by a translation 2 units to the right.

Thus, we conclude that a sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.

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Answer:

\(\frac{2}{\frac{1}{24} }\)

Step-by-step explanation:

2/x = 48

48x = 2

x = (2)/ (1/24)

\(\frac{2}{\frac{1}{24} }\) = 48

The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

3(x + 4) - 11 = 28

3(x + 4) = 28 + 11

3(x + 4) = 39

3x + 12 = 39

3x = 39 - 12

3x = 27

x = 27/3

\(\rule[225]{225}{2}\)

The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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Answer:

4

Step-by-step explanation:

8 halves = 4 whole

The total quantity of cupcakes is 4 units.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

3 halved means 3 divided by 2 which is 3/2 of a cupcake.

4 halves mean 4 divided by 2 which is 4/2 = 2 for friends.

1 more half means 1 divided by 2 which is 1/2 for my other friend.

∴ The total quantity of the cupcakes is (3/2 + 2 + 1/2) = 4.

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Let \(f(x) = x^3 - 2x - 2\). Then differentiating, we get

\(f'(x) = 3x^2 - 2\)

We approximate \(f(x)\) at \(x_1=2\) with the tangent line,

\(f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18\)

The \(x\)-intercept for this approximation will be our next approximation for the root,

\(10x - 18 = 0 \implies x_2 = \dfrac95\)

Repeat this process. Approximate \(f(x)\) at \(x_2 = \frac95\).

\(f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}\)

Then

\(\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}\)

Once more. Approximate \(f(x)\) at \(x_3\).

\(f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}\)

Then

\(\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}\)

Compare this to the actual root of \(f(x)\), which is approximately 1.769292354, matching up to the first 5 digits after the decimal place.

Therefore , the solution of the given problem of unitary method comes out to be Felix's overall tax due is $395.

The task can be finished by applying what was learnt, making use of this access to the world, and fusing all essential components from earlier researchers who used a certain methodology. If the required claim outcome materialises, the entity stated expression in the statement can then either be additionally discovered or both important processes will absolutely miss the expression.

Here,

The tax brackets and rates for single taxpayers are as follows, per the IRS tax tables for 2021:

=> 10% of taxable earnings between $0 and $9,950

=> 12 percent of taxable income between $9,950 and $40,525

=> 22% of tax-exempt income between $40,525 and $86,375

=> 24% of taxable income between $164,925 and $86,375

=> over $164,925 to $209,425 in taxable income, 32%

=> over $209,425 to $523,600 in taxable income, 35%

=> above $523,600 in taxable income, 37%

Felix's yearly gross income is $16,500, and in 2021, the single filer standard deduction is $12,550. His taxable income is thus:

=> $16,500 - $12,550 = $3,950

Felix is subject to 10% tax because his taxable income is less than $9,950. Thus, the amount of his tax is:

=> 10% of $3,950 = $395

Hence, Felix's overall tax due is $395.

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The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.

Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -

x + x + 1 + x + 2 = 12

Performing addition on Left Hand Side of the equation

3x + 3 = 12

Rewriting the equation

3x = 12 - 3

Performing subtraction on Right Hand Side of the equation

3x = 9

x = 9/3

Performing division on Right Hand Side of the equation

x = 3

So, next number = x+1

Second number = 3+1

Second number = 4

Third number = x+2

Third number = 3+2

Third number = 5

Hence, the three consecutive numbers are 3, 4 and 5.

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Answer: A

Step-by-step explanation:

Answer:

yeah is A

Step-by-step explanation:

The price per foot is $3.09

A 3 yard roll of butcher paper costs $9.27

= 9.27/3

= $3.09

Hence the price per foot is $3.09

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Answer:

Step-by-step explanation:

15(1/3) + 19

5 + 19 = 24

Answer:

AFB and BFC

BFC and CFD

CFD and DFE

Step-by-step explanation:

I had just done this and those where the awnsers

Answer:A,C,E

Step-by-step explanation:

The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."

To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:

8b + 5 = 9

To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:

Subtract 5 from both sides to get rid of the constant term:

8b + 5 - 5 = 9 - 5

8b = 4

Divide both sides of the equation by 8 to solve for b:

8b/8 = 4/8

b = 1/2

Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:

8(1/2) + 5 = 9

4 + 5 = 9

Both sides of the equation are equal, confirming that b = 1/2 is the solution.

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Answer:

68

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:68

Step-by-step explanation:

5+9*7=68

Answer:

Width: 13/2 ft.

Length: 12 ft.

Step-by-step explanation:

Let's assume the width is x

This means that the length is 2x-1, because it it one less than double the width.

The formula for the area of a rectangle is length*width, so

(2x-1)*x=78

Now let's solve for x

2x^2-x=78

2x^2-x-78=0

Use the quadratic formula

x=13/2 and x=-6

x cannot be negative, so we can rule out x=-6 and are left with x=13/2.

Substituting x back into our original assumptions, we now know that

The width is x=13/2 and

The length is 2x-1=2(13/2)-1=12

Final answer: The width is 13/2 ft. and the length is 12 ft.

9514 1404 393

Answer:

  12

Step-by-step explanation:

Let x be the smallest number, and y be the middle number. Then the largest number is 2x and the sum is ...

  x + y + 2x = 27   ⇒   y = 27 -3x

The requirement that the middle number is y gives rise to the inequality ...

  x < y < 2x

Substituting for y, we have ...

  x < 27 -3x < 2x

Adding 3x gives us ...

  4x < 27 < 5x

These two inequalities give us the requirement that ...

  27/5 < x < 27/4

  5.4 < x < 6.75

The only whole number in that range is x = 6. So, the greatest number is 2×6 = 12.

The greatest number is 12.

The bearing angle exists 53.49°.

A bearing of 36° corresponds to the corresponding angle of

θ = 90 -36 = 54°

The (x, y) values for the position of the ship after achieving its first heading exist:

\(x_1\) = 12.1 Cos 54° = 7.11 m

\(y_1\) = 12.1 Sin 54° = 9.78 m

Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore

\(x_2\) = 6.1 mi

\(y_2\) = 0 mi

To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:

Δx \(= x_1+x_2\)

= 7.11 mi + 6.1 mi = 13.21 mi

Δy \(=y_1+y_2\)

= 9.78 mi + 0 mi = 9.78 mi

\($r=\sqrt{(x_{total})^2+(y_{total})^2}\)

\(=\sqrt{(13.21mi)^2+(9.78mi)^2}\)

= 16.43 mi

The direction of the displacement vector exists given by

tan θ = Δy/Δx

θ = arc tan (Δy/Δx)

= arc tan (9.78/13.21)

= 36.51°

The question requested for the bearing angle, which exists just this angle subtracted from 90°:

90° - 36.51° = 53.49°.

Therefore, the bearing angle exists 53.49°.

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Answer:

How many apples does Jim have left?

11

How many apples does Ben gain?

18

How many does Ben have in total?

23

Step-by-step explanation:

26 - 15 = 11

15 + 3 =  18 + 5 = 23

Answer:

Step-by-step explanation:

Question 1:

x² = -8x - 7

x² + 8x = -7

(x + 4)² = 9

So the answer is (x + 4)² = 9

Question 2:

(x + 4)² = 9

So x = -4 ± 3

Answer:

1/3

Step-by-step explanation:

4/12÷4÷4=1/3

The answer is 1/3 or 0.333...

Answer: the answer is 1 over 3

Step-by-step explanation:

Answer:

100x100=10,000

A short and easy trick is to multiply only the first number since the rest are zero. So, multiply 1 and 1: 1 x 1. What do you get? 1, of course. Then, add the rest of the zero's after that. In 100, there are two zero's. In 100, there are two zero's. What is two plus two? Well: 2 + 2 = 4 so, four zero's. After that, add the 4 zero's after the 1. One is extremely important in this problem. 1, one zero, 10, two zero's, 100, three zero's, 1,000, and finally, four zero's, 10,000. So, the trick is to multiply the one by the other one, get 1, and add the zero's in the other numbers. This can work as long as it is something like: 10 x 10, 100 x 100, 1,000 x 1,000, or even beyond. Just remember to add the zero's!

Note: This only works with digits similar to the ones listed below.

Notice that they all have a 1 at the front and zero('s) behind them.

1) 10 x 10

2) 100 x 100

3) 1,000 x 1,000

This can continue to over 100 zero's per digit!

The solution to the expression is A = 10000

Given data ,

Let the expression be represented as A

Now , the value of A is

Let the first number be represented as p

The value of p = 100

Let the second number be represented as q

The value of q = 100

So, A = pq

On simplifying the equation , we get

A = p multiplied by the value of q

And , A = 100 x 100

A = 10000

Therefore , the value of A is 10000

Hence , the expression is A = 10000

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